However, the invention presented hereinafter is not restricted to interferometers but can also be used in other measuring devices, wherein various points of a testing volume are moved to in order to generate one or more measurement signals at those locations. In doing so, the testing volume is the quantity of all points which can be moved to and in which measurement signals can be generated. Examples of such measuring devices a deflectometric measuring devices and tactile measuring devices (coordinate measuring devices). Hereinafter, such points will also be referred to as measuring positions.
In this patent application referring interferometers, a distinction is made between so-called classic or conventional interferometers and so-called Tilted Wave Interferometers. The Tilted Wave Interferometer (TWI) is a measuring device for measuring optically smooth, aspherical and freeform surfaces that—different from conventional interferometers—do not work with a test wave (that is emitted by a single light source) but with a plurality of test waves that are tilted relative to each other, said test waves being emitted by various light sources.
For calibrating a TWI the subject matter of publication DE 10 2006 057 606 B4, moves toward various points, that are located in a testing volume of this measuring device and are distinguishable by spatial and/or angular coordinates, with finite accuracy and thus are subject to positioning errors. The points can be distinguished by coordinates in so far as the coordinate system required for the allocation of values of the coordinates during the subsequent measuring process is defined only by the calibration. Measurement signals are generated in the respective points, and parameters of a mathematical model of the measuring device are determined based on the measurement signals and the spatial and/or angular coordinates.
Among other things, interferometers are used for measuring optically smooth surfaces. In so doing, an optically smooth surface is a specular reflecting boundary surface or a smooth, refractive boundary surface of a transparent object.
In the course of the interferometric measurement of such boundary surfaces, a test wave (object wave) and a reference wave coherent with respect to said test wave are generated. The test wave and the reference wave are preferably generated from coherent light of one and the same light source, this being accomplished with the use of a beam splitter, for example. The test wave is reflected or refracted by the boundary surface and subsequently superimposed with a reference wave on a detector, for example a light-sensitive chip of a camera, wherein said reference wave has not experienced any interaction with the object or is a known modified copy of the test wave as is the case, for example, in shearing interferometry. The optical path lengths passed by both waves up to their superimposition on the detector depend on influences of the respective beam guide in the interferometer and the influence of the object on the test wave. The resulting interference image is thus undesirably ambiguous. The objective of a calibration is the elimination of the influence of the beam guide of the interferometer.
To be able to eliminate this influence it has been known to measure objects to be measured (test samples) in so-called null test configurations, which adapt the rays in such a manner that they are again incident perpendicularly on the sample or compare them to the highly accurate known master surfaces. For example, the adaptation is accomplished by a CGH or by a refractive compensation optics. The influences of the beam guide then occur on the master surface, as well as on the sample, in identical form and can thus be basically eliminated during the evaluation due to the formation of a difference. The path length differences that remain with such an evaluation then only provide an image of the deviations of the sample from the master surface. This type of calibration is also referred to as null test and is suitable, in particular, for spherical samples because spherical master surfaces can be provided with comparatively minimal effort.
Null tests on aspheres require special refractive or diffractive optics adapted to the shape of the aspheres which is undesirable because of the manufacturing expense connected therewith.
The aforementioned known method works without such master surfaces. In that case, the calibration is based on a description of the interferometric measuring devices, namely in the form of the Black Box mathematical model. This mathematical model requires a precise knowledge of the optical paths in the interferometer. This model, or the description of the interferometer in the form of the Black Box mathematical model, allows a calculation of the optical path length—OPL) existing between the light source and the detector for any conceivable light beam that passes through the testing volume and, in so doing, is reflected, refracted or diffracted on the object to be measured.
For calculating these path lengths, the OPLs are described by multidimensional polynomials. The polynomial coefficients acting as model parameters are initially calculated for an ideal interferometer. Deviations (aberrations) of the real interferometer from the ideal interferometer are determined by measurements performed on a known reference object, and the calculated polynomial coefficients are calibrated therewith. Here, a calibration is understood to mean an adaptation of the coefficients, this being accomplished in that the OPLs in the real interferometer can be correctly calculated by the multidimensional polynomials with adapted coefficients. Hence, the objective of the calibration is to determine the polynomial coefficients in such a manner that they allow the most accurate possible description of the optical paths in the real interferometer. In so doing, the reference object is measured at several points (measuring positions) in the testing volume, and the Black Box parameters (i.e., the polynomial coefficients) of the real interferometer are determined therefrom by means of an optimizing process.
Upon completion of the calibration it is possible with the aid of the Black Box model to correctly calculate each and every optical path in the interferometer. Because the polynomial coefficients are known, there results a description of the interferometer that allows the calculation of the optical path length (OPL) from the source to the detector—for each conceivable light beam in the testing volume—when the influence of the object to be examined is known. Consequently, the influence of the interferometer on the measurement result can be determined and be mathematically eliminated as a result.
In order to be able to determine the Black Box parameters during the calibration, the optimization problem to be solved with the optimizing process must be clearly defined. On the one hand, this means that the available degrees of freedom for optimization should be such so as to not form any ambiguities, i.e., that it is not possible to describe the same condition with different parameter sets.
On the other hand, however, there must be sufficient degrees of freedom to allow the algorithm to find the correct solution; and this solution must be attainable within the available solution range. In so doing, the solution range is understood to mean the quantity of all possible values of the Black Box parameters and the polynomial coefficients, respectively.
Furthermore, the information that acts as the input data set for calibration must be selected in such a manner that there is only one possible, namely physically relevant, solution. Otherwise, there is the risk that, instead of the physically correct solution, another local minimum is found. The previous calibration method exhibits a few shortcomings in this regard, these potentially resulting in flawed calibrations.
Against this background, the object of the present invention is the further improvement of the method mentioned hereinabove.